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Simplifying x2 + 10x + 21 = 961 Reorder the terms: 21 + 10x + x2 = 961 Solving 21 + 10x + x2 = 961 Solving for variable 'x'. Reorder the terms: 21 + -961 + 10x + x2 = 961 + -961 Combine like terms: 21 + -961 = -940 -940 + 10x + x2 = 961 + -961 Combine like terms: 961 + -961 = 0 -940 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '940' to each side of the equation. -940 + 10x + 940 + x2 = 0 + 940 Reorder the terms: -940 + 940 + 10x + x2 = 0 + 940 Combine like terms: -940 + 940 = 0 0 + 10x + x2 = 0 + 940 10x + x2 = 0 + 940 Combine like terms: 0 + 940 = 940 10x + x2 = 940 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 940 + 25 Reorder the terms: 25 + 10x + x2 = 940 + 25 Combine like terms: 940 + 25 = 965 25 + 10x + x2 = 965 Factor a perfect square on the left side: (x + 5)(x + 5) = 965 Calculate the square root of the right side: 31.064449134 Break this problem into two subproblems by setting (x + 5) equal to 31.064449134 and -31.064449134.Subproblem 1
x + 5 = 31.064449134 Simplifying x + 5 = 31.064449134 Reorder the terms: 5 + x = 31.064449134 Solving 5 + x = 31.064449134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 31.064449134 + -5 Combine like terms: 5 + -5 = 0 0 + x = 31.064449134 + -5 x = 31.064449134 + -5 Combine like terms: 31.064449134 + -5 = 26.064449134 x = 26.064449134 Simplifying x = 26.064449134Subproblem 2
x + 5 = -31.064449134 Simplifying x + 5 = -31.064449134 Reorder the terms: 5 + x = -31.064449134 Solving 5 + x = -31.064449134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -31.064449134 + -5 Combine like terms: 5 + -5 = 0 0 + x = -31.064449134 + -5 x = -31.064449134 + -5 Combine like terms: -31.064449134 + -5 = -36.064449134 x = -36.064449134 Simplifying x = -36.064449134Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.064449134, -36.064449134}
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